Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, e
from proveit.logic import InSet
from proveit.numbers import Add, Exp, LessEq, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import Pfail, _e_domain

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(e, Conditional(LessEq(Pfail(e), Add(frac(one, Mult(two, e)), frac(one, Mult(four, Exp(e, two))))), InSet(e, _e_domain))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(e \mapsto \left\{\left[P_{\rm fail}\right]\left(e\right) \leq \left(\frac{1}{2 \cdot e} + \frac{1}{4 \cdot e^{2}}\right) \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 40 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	40, 11
9	Operation	operator: 12 operand: 40
10	Operation	operator: 38 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprTuple	40
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	46, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 38 operands: 23
20	ExprTuple	46, 24
21	Literal
22	ExprTuple	46, 25
23	ExprTuple	26, 27
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 36 operands: 31
27	Operation	operator: 44 operand: 41
28	ExprTuple	41, 40
29	Literal
30	ExprTuple	33, 34
31	ExprTuple	41, 35
32	ExprTuple	41
33	Literal
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42, 43
40	Variable
41	Literal
42	Literal
43	Operation	operator: 44 operand: 46
44	Literal
45	ExprTuple	46
46	Literal